分岔

Then we use theory ofnormal form and universal unfolding and Melnikov's and Petrov's methods to studydegenerate bifurcations of codimension three and global bifurcations in the averagedequations.

然后利用规范形理论、普适开折理论、Petrov方法和Melnikov方法研究了平均系统的余维3退化分岔和全局分岔。

First we use the method of multiple scales tostudy local bifurcations of this system and obtain transition sets and bifurcating responsecurves.Then we use theory of normal form and universal unfolding and Melnikov'smethod to study further degenerate bifurcations of codimension two and globalbifurcations.

然后利用规范形理论、普适开折理论和Melnikov方法进一步研究了余维2退化分岔和全局分岔，并且获得了一些有意义的结果，提出了不完全普适开折的问题。

The loca l bifurcation characteristic near by codimension two bifurcation point is discus sed,which testifies that the local dynamical behavior of map fmay be known under the condition of cod.

通过分析范式在余维二分岔点附近的局部分岔行为，可以了解映射f在余维二分岔条件下的局部动力学行

The aim of this paper is to demonstrate the use of the open loop control to change the nonlinear system parameters in order to obtain a desired equilibrium bifurcation diagram.

利用开环控制来改变非线性系统的分岔参数，使之获得理想的平衡点分岔图。

Limit induced bifurcation by generator excitation voltage limit was studied, the critical limit was presented and a mechanism of LIB was proposed.

研究由于发电机励磁电压限制导致的极限诱导分岔，发现临界限值的存在并提出一种极限诱导分岔的机理解释。

In this thesis,the voltage stability boundary is the combined boundary which correspond to Saddle-node bifurcations and Hopf bifurcations.The closest Hopf bifurcation point is found through the proposed iterative method under the assumption that the Hopf hypersurface is continuous and convex.

因此在本论文中，在多维参数空间下，将稳定边界推广到鞍点和Hopf分岔点构成的混合稳定边界，探索性寻求Hopf分岔超平面的法向量，采用迭代算法求取系统发生最近振荡型电压失稳的负荷增长方式。

This paper applied an algebraic criterion to identify Hopf bifurcation for the six-dimensional red blood cell survival model, and analyzed stability of the generated limit circle by using projection method.

本文应用任意阶Hopf分岔代数判据对六阶红细胞存活模型的Hopf分岔点进行判定，同时利用投影法判断是否存在稳定极限环。

The critical value of Hopf bifurcation was calculated, and the stability of the limit cycle was discussed. The bifurcation diagram of the system was obtained by the fourth order Runge-Kutta method.

定性分析了系统定态的存在性和稳定性，讨论了系统的Hopf分岔，得到了系统的Hopf分岔参数值，并判断了极限环的稳定性。

The joint effect of active and reactive power on the voltage stability of a typical power system was considered by analysing the two parameter bifurcation problem related to nonlinear oscillation phenomena. Numerically, as the active power P1 increases, the Hopf points get closer and eventually coincide at P1=1.455 43 the cyclic fold curve gets closer and closer to the Hopf curve and finally intersects the Hopf curve at a singular point the period-doubling points also get closer and finally coincide at P1≈0.65. The stability behaviour is pre-determined using the normal form approach near the limit point of the Hopf curve. Hence, in the power system attention should be paid to both the consumption of active power and the decrease in the reactive power to prevent nonlinear oscillations. A controller can be designed to absorb some active power and to avoid the nonlinear oscillations that damage the system components.

针对一个典型的单机无穷大电力系统，通过分析系统的双参数分岔的非线性振荡现象，综合考虑有功和无功功率对电压稳定性的影响数值分析表明，随着有功功率的增加，电力系统的Hopf点越来越靠近，最终合为一点在P1=1.455 43处同时圈折cyclic fold 曲线也越来越靠近Hopf曲线，并在Hopf曲线的稳定与不稳定临界点处与Hopf曲线相交倍周期分岔点也随着越来越靠近，最终在P1≈0.65 合为一点应用正规形理论方法，初步确定了Hopf曲线极限点附近的稳定性态因而，电力系统应注意让负荷利用有功功率，减少无功功率的产生以防止非线性振荡另外，可以设计一个稍微吸收网络的有功功率的控制器，以避免因周期振荡而造成电力系统仪器的损坏或电压崩溃

The direction and stability of bifurcation are determined by the normal form theory and center manifold theorem. Results of some computer simulations are displayed graphically.

利用中心投影方法我们给出了分岔方向和稳定性的计算公式，并利用计算机对Neimark-Sacker-分岔进行了模拟验证。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。